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          <h1 class="post-title" itemprop="name headline">PAT A1123 . Is It a Complete AVL Tree (30)</h1>
        

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        <p>An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.</p>
<p><img src="https://www.patest.cn/upload/mr_ohesevgnyny.jpg" alt="请输入图片描述"><br><img src="https://www.patest.cn/upload/mr_ohesfdbkaep.jpg" alt="请输入图片描述"><br><img src="https://www.patest.cn/upload/mr_oheseymzi13.jpg" alt="请输入图片描述"><br><img src="https://www.patest.cn/upload/mr_ohesfjddti2.jpg" alt="请输入图片描述"></p>
<p>Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.</p>
<p>Input Specification:</p>
<p>Each input file contains one test case. For each case, the first line contains a positive integer N (&lt;= 20). Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.</p>
<p>Output Specification:</p>
<p>For each test case, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print “YES” if the tree is complete, or “NO” if not.</p>
<p>Sample Input 1:<br>5<br>88 70 61 63 65<br>Sample Output 1:<br>70 63 88 61 65<br>YES<br>Sample Input 2:<br>8<br>88 70 61 96 120 90 65 68<br>Sample Output 2:<br>88 65 96 61 70 90 120 68<br>NO<br><figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br></pre></td><td class="code"><pre><span class="line">#include &lt;stdio.h&gt;</span><br><span class="line">#include &lt;algorithm&gt;</span><br><span class="line">#include &lt;vector&gt;</span><br><span class="line">#include &lt;queue&gt;</span><br><span class="line">using namespace std;</span><br><span class="line">vector&lt;int&gt; layer;</span><br><span class="line"></span><br><span class="line">struct node&#123;</span><br><span class="line">    int v,height;</span><br><span class="line">    int order;</span><br><span class="line">    node *lchild,*rchild;</span><br><span class="line">&#125;;</span><br><span class="line">node* newNode(int v)&#123;</span><br><span class="line">    node* Node = new node;</span><br><span class="line">    Node-&gt;v = v;</span><br><span class="line">    Node-&gt;height = 1;</span><br><span class="line">    Node-&gt;lchild = Node-&gt;rchild = NULL;</span><br><span class="line">    return Node;</span><br><span class="line">&#125;</span><br><span class="line">int getHeight(node* root)&#123;</span><br><span class="line">    if(root == NULL) return 0;</span><br><span class="line">    return root-&gt;height;</span><br><span class="line">&#125;</span><br><span class="line">int getBalanceFactor(node* root)&#123;</span><br><span class="line">    return getHeight(root-&gt;lchild)-getHeight(root-&gt;rchild);</span><br><span class="line">&#125;</span><br><span class="line">void updateHeight(node* root)&#123;</span><br><span class="line">    root-&gt;height=max(getHeight(root-&gt;lchild),getHeight(root-&gt;rchild))+1;</span><br><span class="line">&#125;</span><br><span class="line">void L(node* &amp;root)&#123;</span><br><span class="line">    node* temp = root-&gt;rchild;</span><br><span class="line">    root-&gt;rchild = temp-&gt;lchild;</span><br><span class="line">    temp-&gt;lchild = root;</span><br><span class="line">    updateHeight(root);</span><br><span class="line">    updateHeight(temp);</span><br><span class="line">    root = temp;</span><br><span class="line">&#125;</span><br><span class="line">void R(node* &amp;root)&#123;</span><br><span class="line">    node* temp = root-&gt;lchild;</span><br><span class="line">    root-&gt;lchild = temp-&gt;rchild;</span><br><span class="line">    temp-&gt;rchild = root;</span><br><span class="line">    updateHeight(root);</span><br><span class="line">    updateHeight(temp);</span><br><span class="line">    root = temp;</span><br><span class="line">&#125;</span><br><span class="line">void insert(node* &amp;root,int v)&#123;</span><br><span class="line">    if(root == NULL)&#123;</span><br><span class="line">        root = newNode(v);</span><br><span class="line">        return;</span><br><span class="line">    &#125;</span><br><span class="line">    if(v &lt; root-&gt;v)&#123;</span><br><span class="line">        insert(root-&gt;lchild,v);</span><br><span class="line">        updateHeight(root);</span><br><span class="line">        if(getBalanceFactor(root) == 2)&#123;</span><br><span class="line">            if(getBalanceFactor(root-&gt;lchild) == 1)&#123;//LL</span><br><span class="line">                R(root);</span><br><span class="line">            &#125;</span><br><span class="line">            else if(getBalanceFactor(root-&gt;lchild) == -1)&#123;//LR</span><br><span class="line">                L(root-&gt;lchild);</span><br><span class="line">                R(root);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    else&#123;</span><br><span class="line">        insert(root-&gt;rchild,v);</span><br><span class="line">        updateHeight(root);</span><br><span class="line">        if(getBalanceFactor(root) == -2)&#123;</span><br><span class="line">            if(getBalanceFactor(root-&gt;rchild) == -1)&#123;//RR</span><br><span class="line">                L(root);</span><br><span class="line">            &#125;</span><br><span class="line">            else if(getBalanceFactor(root-&gt;rchild) == 1)&#123;//RL</span><br><span class="line">                R(root-&gt;rchild);</span><br><span class="line">                L(root);</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line">node *last = new node;</span><br><span class="line">void layerOrder(node* root,vector&lt;int&gt; &amp;vi)&#123;</span><br><span class="line">    queue&lt;node*&gt; q;</span><br><span class="line">    q.push(root);</span><br><span class="line">    root-&gt;order = 1;</span><br><span class="line">    while (!q.empty()) &#123;</span><br><span class="line">        node* now = q.front();</span><br><span class="line">        last = now;</span><br><span class="line">        q.pop();</span><br><span class="line">        vi.push_back(now-&gt;v);</span><br><span class="line">        if (now-&gt;lchild != NULL) &#123;</span><br><span class="line">            q.push(now-&gt;lchild);</span><br><span class="line">            now-&gt;lchild-&gt;order = 2 * now-&gt;order;</span><br><span class="line">        &#125;</span><br><span class="line">        if (now-&gt;rchild != NULL) &#123;</span><br><span class="line">            q.push(now-&gt;rchild);</span><br><span class="line">            now-&gt;rchild-&gt;order = 2 * now-&gt;order + 1;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line">int main()&#123;</span><br><span class="line">    int n, temp;</span><br><span class="line">    scanf(&quot;%d&quot;, &amp;n);</span><br><span class="line">    node* root = NULL;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        scanf(&quot;%d&quot;, &amp;temp);</span><br><span class="line">        insert(root, temp);</span><br><span class="line">    &#125;</span><br><span class="line">    layerOrder(root, layer);</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        printf(&quot;%d&quot;, layer[i]);</span><br><span class="line">        if (i &lt; n - 1) printf(&quot; &quot;);</span><br><span class="line">        else printf(&quot;\n&quot;);</span><br><span class="line">    &#125;</span><br><span class="line">    if (last-&gt;order == n) &#123;</span><br><span class="line">        printf(&quot;YES\n&quot;);</span><br><span class="line">    &#125;else&#123;</span><br><span class="line">        printf(&quot;NO\n&quot;);</span><br><span class="line">    &#125;</span><br><span class="line">    return 0;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></p>

      
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